Use our free GCF of Fractions Calculator tool to compute the GCF of 75/28, 928/73, 731/756 i.e 1/55188 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/28, 928/73, 731/756.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 75/28,928/73,731/756
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 75/28,928/73,731/756, numerators are 75,928,731
Denominators are 28,73,756
The GCF of 75,928,731 is 1 .
LCM of 28,73,756 is 55188.
The greatest common factor of 75/28,928/73,731/756 = [GCF of 75,928,731]/[LCM of 28,73,756]= 1/55188
Therefore, the GCF of 75/28,928/73,731/756 is 1/55188.
To find the highest common factor of 75,928,731, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 928 are 1, 2, 4, 8, 16, 29, 32, 58, 116, 232, 464, 928
The factors of 731 are 1, 17, 43, 731
The HCF of 75,928,731 is 1.
Lets's calculate GCF of 75,928,731
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 928
:1,2,4,8,16,29,32,58,116,232,464,928
Now, list down the factors of 731
:1,17,43,731
Greatest Common Factor
We found the factors 75,928,731 . The biggest common factor number is the GCF number.
So the greatest common factor 75,928,731 is 1.
Lets's calculate LCM of 28,73,756
2 | 28, 73, 756 |
2 | 14, 73, 378 |
7 | 7, 73, 189 |
1, 73, 27 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 1 x 73 x 27 = 55188
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/55188
Therefore, the GCF of Fractions 75/28,928/73,731/756 is 1/55188
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 28,73,756 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,73,756) = 1
common factors(in case of two or more numbers have common factors) = 28
GCF(28,73,756) x common factors =1 x 28 = 28
LCM(28,73,756) = ( 28 × 73 × 756 ) / 28
LCM(28,73,756) = 1545264 / 28
LCM(28,73,756) = 55188
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 75,928,731?
The HCF of 75,928,731 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 75/28, 928/73, 731/756?
Answer: GCF of Numerators as per given numbers 75/28, 928/73, 731/756 is
GCF of Numerators i.e. for 75,928,731 is 1
LCM of denominators i.e. for 28,73,756 is 55188.
Thus, GCF of Fractions is 1/55188.Finally, GCF of Fractions for 75/28, 928/73, 731/756 is 1/55188.